A mixed double tennis game is to be played between two teams
(each team consists of one male and one female ).There are
four married couples . No team is to consist of a husband and
{his wife. What is the maximum number of games that can be played.

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A mixed double tennis game is to be played between two teams
(each team consists of one male and one female ).There are
four married couples . No team is to consist of a husband and
{his wife. What is the maximum number of games that can be played.

Mathematics

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mathmath333

2 years ago

\(\large \color{black}{\begin{align}
& \normalsize \text{A mixed double tennis game is to be played between two teams }\hspace{.33em}\\~\\
& \normalsize \text{(each team consists of one male and one female ).There are }\hspace{.33em}\\~\\
& \normalsize \text{four married couples . No team is to consist of a husband and }\hspace{.33em}\\~\\
& \normalsize \text{his wife. What is the maximum number of games that can be played. }\hspace{.33em}\\~\\
& a.)\ 12 \hspace{.33em}\\~\\
& b.)\ 21 \hspace{.33em}\\~\\
& c.)\ 36 \hspace{.33em}\\~\\
& d.)\ 42 \hspace{.33em}\\~\\
\end{align}}\)

mathstudent55

2 years ago

Husband is A, B, C, D
Wife is 1, 2, 3, 4
Married couples are: A1, B2, C3, D4
For each line below, the pair in the first column can play a match with each pair following it. For example, for the first line below, there can be matches: A2 vs B1, A2 vs B3, A2 vs B4, etc.
A2 B1 B3 B4 C1 C4 D1 D3
A3 B1 B4 C1 C2 C4 D1 D2
A4 B1 B3 C1 C2 D1 D2 D3
It looks like 21 different matches.

4 man and 4 women can form 16 teams. 4 teams are forbidden since there are 4 married couples. There are 12C2=66 unique ways of choosing 2 elements from a set with 12 elements. Therefore 12 teams can have 12C2=66 ways of matching and game.

mathstudent's answer is correct, but i m looking for a short answer rather than listing all as mathstudent did.

anonymous

2 years ago

@thomas5267 only problem is that A2 cannot play A3. In your scheme, these are indeed different teams but they cannot play each other.
For a given team, it has only 6 other teams against which it can compete. then you have to count repeats as well.

anonymous

2 years ago

oops, 7 other teams against which it can compete

thomas5267

2 years ago

Oh crap!

mathstudent55

2 years ago

@thomas5267
The problem states that a man and his wife cannot form a team, so you can't form 16 teams.

thomas5267

2 years ago

Computer says there are 42 combinations. I calculated it using brute force.